A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson--Nernst--Planck systems
Numerical Analysis
2016-12-21 v1
Abstract
We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivities of numerical solutions are enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.
Keywords
Cite
@article{arxiv.1611.00082,
title = {A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson--Nernst--Planck systems},
author = {Hailiang Liu and Zhongming Wang},
journal= {arXiv preprint arXiv:1611.00082},
year = {2016}
}